{"paper":{"title":"A note on the security of CSIDH","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Annamaria Iezzi, Jean-Fran\\c{c}ois Biasse, Michael J. Jacobson Jr","submitted_at":"2018-06-10T13:19:20Z","abstract_excerpt":"We propose an algorithm for computing an isogeny between two elliptic curves $E_1,E_2$ defined over a finite field such that there is an imaginary quadratic order $\\mathcal{O}$ satisfying $\\mathcal{O}\\simeq \\operatorname{End}(E_i)$ for $i = 1,2$. This concerns ordinary curves and supersingular curves defined over $\\mathbb{F}_p$ (the latter used in the recent CSIDH proposal). Our algorithm has heuristic asymptotic run time $e^{O\\left(\\sqrt{\\log(|\\Delta|)}\\right)}$ and requires polynomial quantum memory and $e^{O\\left(\\sqrt{\\log(|\\Delta|)}\\right)}$ classical memory, where $\\Delta$ is the discrim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03656","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}